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KN phase shifts in chiral quark model. F. Huang, Z.Y. Zhang, Y.W. Yu (Institute of High Energy Physics, Beijing, China). Outline. Motivations Formulation The model Determination of parameters Results discussions Summary. Motivations. To extend our model to study BM interactions - PowerPoint PPT Presentation
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KN phase shifts in chiral quark model
F. Huang, Z.Y. Zhang, Y.W. Yu
(Institute of High Energy Physics, Beijing,
China)
Motivations Formulation
The model Determination of parameters
Results discussions Summary
Outline
Motivations• To extend our model to study BM
interactionso NPQCD effect is important; QCD-inspired
models are still neededo Our model works well for NN and NYo To extend our model to study BM
interactions; Start with KN in which annihilation is simple
• To get a better understanding of KN
interactiono Most of previous works based on CQM failed
to accurately reproduce the KN phase shiftso Can we reproduce KN phase shifts in our
model ?
Formulation (1) the modelThe Hamiltonian of KN system
Generalize the idea of SU(2) σ model to SU(3)f case
Clearly, HIch is invariant under the infinitesimal
chiral SU(3)LSU(3)R transformation.
From HIch, the SU(3) chiral-field-induced
quark-quark potentials can be derived
For KN, there are alsoqq interactions
For KN system,qq can only annihilate into kaon
Ck is adjusted to fit the mass of kaon
The exchange diagrams forqq
The annihilation diagrams forqq
Formulation (2) parameters fitting
• Input: bu=0.5 fm, mu=313 MeV, ms=470 MeV
• The chiral field coupling constant
• Mesons’ masses: experimental values Except mσ (adjustable parameter), mσ=675 MeV
• Λ-1=0.18 fm, close to chiral symmetry breaking scale
• gu and gs, determined by mΔ-mN and mΣ-mΛ
• Parameters of Vconf, fitted by baryons’ masses and their stability conditions
We consider the mixing between the flavor singlet and octet mesons
The mixing of scalar meson is still an open problem
About the mixing angle
PS= –23
Ⅰ S≈ 35Ⅱ S= –18
Y.B. Dai, Y.L. Wu, hep-ph/0304075
Model parametersmσ 980=׳ MeV, m=980 MeV
mε=980 MeV, mσ=675 MeV
m=138 MeV, m=495 MeV
m=549 MeV, mη 957=׳ MeV
Λ=1100 MeV
The masses of baryons
Results discussions• RGM calculation
• Conventional notation LI 2J
About the mixing of σ0 and σ8
The attraction of σ is reduced in both of these two cases
Ⅰ S≈ 35Ⅱ S= –18
We took two possible values of S
Influence of the annihilation
The numerical phase shifts scarcely have changes when we omit the annihilation part entirely.
The annihilation part coming form S-channel acts in the very short range, so it plays a non-significant role in KN scattering process.
The annihilation diagrams forqq
Comparing with recent RGM study
S. Lemaire et al, NPA 714 (2003) 265
gluon+++confinement, RGM calculation
Summary
The chiral SU(3) quark model is extended to includeq
KN scattering process is studied using RGM
Our results achieve a considerable improvement on theoretical phase shifts comparing with others’ worksA reasonable interaction between K and N
can be obtained from the chiral SU(3) quark model when the mixing of σ0 and σ8 is
considered and mσ is taken to be 675 MeV
The end
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